I'm afraid parking and traffic contraventions enforcement is complex and goes a long way to explain why so many people just cough-up immediately on receiving a PCN, (>95% in fact). Most people have no knowledge of the laws and regulations that govern council enforcement, and assume that councils know it all. This is very, very, far from the truth !
However, your position has lead to doubt even amongst those of us who try to give good advice as you will have seen.
You were served with a PCN for parking off-carriageway, and this has been an offence in London since the 70s, and requires no lines or signs. Yet you were parked directly adjacent to double-yellow lines that mean "No Waiting" (aka parking). So the CEO had a choice of contraventions to use when issuing a PCN. He chose to serve one based on parking off-carriageway, not not one based on parked where not permitted, (the double-yellow lines). YOu might ask why. Well, there are two exemptions to the double-yellow lines, (1) loading/unloading, and (2) boarding/alighting passengers. Your circumstances fit (2). There are no exemptions to off-carriageway parking, apart from a loading requirement needing such parking.
The assumption the CEO made is that the way the road has been resurfaced and "improved", with the double-yellow lines moved, means that the turning point is no longer carriageway, but an off-carriageway part of the road, (a road is everything between the property boundaries each side, incl carriageway, verges and footways).
HCA says the layout shows where you parked is not carriageway, but if that is so, why has the space got bollards round it to mark it off specially ? Why any bollards at all ? My own view is that the turning space remains carriageway for turning purposes, and the council are in error. HCA disagrees with me, and the only way to finally determine the issue is to look at what the TRO says. That is the decider, because the new road layout must be reflected in the TRO. If it is, you lose, if it isn't, you win.